Boiling heat transfer by phase-field method

In this work, we propose and test the validity of a phase-field method tailored specifically for modeling boiling heat transfer phenomena. The method relies on a direct solution of the Navier-Stokes equations coupled with a phase-field model and the energy equation. The continuity and Navier-Stokes equations have been modified introducing a source term that accounts for the phase-change phenomena. Likewise, in the conservative Allen-Cahn equation (phase-field method) a source term that accounts for the expansion produced by the boiling process is introduced. The system of governing equations is solved using a projection-correction method and equations are discretized using a finite difference approach. To efficiently solve the Poisson pressure equation, we employ a splitting technique, enabling the utilization of FFT-based direct solvers. The validity of the proposed method is studied by considering the Stefan problem, where the phase change is driven by superheated vapor, and the the adsorption problem, where the phase change is induced by superheated liquid. For both benchmarks, the present method well matches with analytical and archival literature results for a wide range of vapor-to-liquid density ratios, from ρv/ρl = 1 down to ρv/ρl = 0.001 (where ρv identifies the vapor density and ρl the liquid density). Finally, the proposed method is used to investigate the growth of a vapor bubble in superheated liquid and the film boiling process, providing physical insights into these complex phenomena.